(x-3)(x-3)=289

Solution for (x-3)(x-3)=289 equation:

(x-3)(x-3)=289

We move all terms to the left:

(x-3)(x-3)-(289)=0

We multiply parentheses ..

(+x^2-3x-3x+9)-289=0

We get rid of parentheses

x^2-3x-3x+9-289=0

We add all the numbers together, and all the variables

x^2-6x-280=0

a = 1; b = -6; c = -280;
Δ = b2-4ac
Δ = -62-4·1·(-280)
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-34}{2*1}=\frac{-28}{2}
=-14
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+34}{2*1}=\frac{40}{2}
=20
$